Linear techniques for dynamic chemical process simulation and direct digital control algorithm implementation

Digital simulation algorithms are studied with a goal of establishing guidelines to select accurate methods for simulating the dynamic response of linear continuous models. Linear models play a large role in many simulation applications, especially in applied industrial process simulation and control. To date no in depth study can be found in the literature where digital simulation techniques are surveyed and compared to provide any guidelines.

One major problem in digital computer simulation is the conversion of a process oriented model to a digital computer oriented model. In other words, algorithms are needed to convert the continuous process equations into difference equations which can be eventually expressed as recursive formulas and implemented in digital computers. Numerical integration schemes are commonly and widely used; however, with respect to linear models these methods may be unnecessary and inefficient. Moreover, the requirememt of relatively small simulation step size to keep the numerical integration schemes stable may limit their applications. A major concept in this work is to capitalize on the use of methods that take advantage of the models' linearity.

Six optimal discretization methods were applied to the simulation of three transfer function models under the criteria of best matching the time domain transient response. This study indicated the Taylor method, a relatively new technique, provides perhaps the best discretization algorithm in the survey. Also two input approximation methods, one was the popular zero-order hold with phase compensation, gave good results.

Also presented is a new procedure for calculating the discrete transition state matrix, P, and discrete input matrix, Q, which are needed to solve state space models. The new procedure formulates an augmented matrix whose matrix exponential provides both P and Q even when the state transition matrix is singular.